我们将结果应用于具有未知分布的先知秘书问题，但可以访问每个分布中的单个样本。我们的保证改进了1-1 / e这个问题，这是目前最着名的保证，只适用于i.i.d.案件。
原文标题：The Two-Sided Game of Googol and Sample-Based Prophet Inequalities
原文摘要：The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. We consider a variant of the problem and explore its connections to data-driven online selection. Specifically, we are givenncards with arbitrary non-negative numbers written on both sides. The cards are randomly placed onnconsecutive positions on a table, and for each card, the visible side is also selected at random. The player sees the visible side of all cards and wants to select the card with the maximum hidden value. To this end, the player flips the first card, sees its hidden value and decides whether to pick it or drop it and continue with the next card.
We study algorithms for two natural objectives. In the first one, as in the secretary problem, the player wants to maximize the probability of selecting the maximum hidden value. We show that this can be done with probability at least0.45292. In the second one, similar to the prophet inequality, the player maximizes the expectation of the selected hidden value. We show a guarantee of at least0.63518with respect to the expected maximum hidden value.
Our algorithms result from combining three basic strategies. One is to stop whenever we see a value larger than the initialnvisible numbers. The second one is to stop the first time the last flipped card's value is the largest of the currentlynvisible numbers in the table. And the third one is similar to the latter but it additionally requires that the last flipped value is larger than the value on the other side of its card.
We apply our results to the prophet secretary problem with unknown distributions, but with access to a single sample from each distribution. Our guarantee improves upon1−1/efor this problem, which is the currently best known guarantee and only works for the i.i.d. case.
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